The Form of Practical Inference

The argument is relatively straightforward — relative, that is, to the average Anscombe argument. Suppose we have the inference pattern:

A→B

B→C

A

Therefore: C.

This looks like a piece of theoretical reasoning. From A, and from the relevant entailments, we’re able to conclude C. Suppose that A is “the potatoes have been in the oven for 20 minutes”, B is “the potatoes are cooked”, and C is “the potatoes are ready to eat”. If we know that A, we know that A entails B, and we know that B entails C, then we know that C.

Suppose, on the other hand, that C is something we‘re aiming at bringing about (we’re cooking potatoes). We can use the same inference to decide to bring about A. Now the inference looks like this:

Aiming at: C.

A→B

B→C

Therefore: bring it about that A.

The formal inference is the same. What makes it practical is nothing about the logical form, but only what we’re using that inference for.

What prevents some logicians from seeing this, says Anscombe, is a misguided idea about necessity. In the theoretical case, there appears to be a logical compulsion that is absent in the practical case. No reasonable person can accept the premises without accepting the conclusion. In the practical case, by contrast, there does not appear to be the same necessity. There might, for all the inference shows, be a way to bring it about that C without bringing it about that A. Thus aiming at bringing about C does not compel bringing about A.

Anscombe argues that this is a false distinction. If “compulsion” means “compulsion according to the norms of inference”, then we can say that the norms of practical inference compel bringing it about that A when C is desired, just as the norms of theoretical inference compel believing C when A is believed. It might not represent the only way to bring about C, but then the theoretical inference might not represent the only way to conclude that C. Meanwhile if “compulsion” means “psychological compulsion”, then we must admit that neither the theoretical nor the practical inference is compelling: people reason badly both theoretically and practically.

There is much more to be said, and Anscombe deals with various objections. But the conclusion is that the form of the inference is the same in the practical and in the theoretical case. What makes the difference between practical and theoretical reasoning is what we use the inference for rather than its form.

Anscombe is discussing what Aristotle calls “practical syllogism” in the ‘common books’ of the Nichomachean and Eudemian Ethics. Aristotle uses “συλλογισμος” to mean simply “reasoning”; there is no strong compulsion to suppose him to be talking about the more specific syllogistic theory of inference found in the Prior Analytics. And yet the examples that Aristotle gives of practical syllogisms can be read in line with that theory.

Anscombe moves right away to a logic of propositions rather than to a logic of terms. But Aristotle’s examples can be analysed in terms of the logic of terms proposed in his syllogistic. Here is one of them (more or less):

As stated, the syllogism clearly isn’t valid under the rules of the Prior Analytics. But the obvious reason for this obscures the more interesting reason.

The obvious reason is that the conclusion mentions something that isn’t in any of the premises: my action of eating something. If the argument is a sorites, then the conclusion should be: “I benefit from dry food”. The moral philosopher can bring in all sorts of Humean quibbles about whether this is sufficient on its own to compel any action.

But the logician might be at least equally interested in the way the terms are divided up. Let me represent the inference, with the modified conclusion, putting subject-terms in round brackets and predicate-terms in square brackets. The copulas I leave out. Then we have:

(Human beings) [benefit from dry food].

(I) [human being].

(This bread) [dry food].

Therefore: (I) [benefit from dry food].

For the syllogism to be valid (as a sorites), we would need four terms, to match our four propositions. But what we have here is five terms. “Dry food” is not the same term as “benefit from dry food”. If we treat the two terms as equivalent, we can end up with one of the following valid but nonsensical soriteses:

Humans beings benefit from dry food.

I am a human being.

Benefit from dry food is this bread.

Therefore I am this bread.

Or:

Human beings are dry food.

I am a human being.

This bread is dry food.

Therefore I am this bread.

The conclusion is the same in each sorites. And it is decidedly not what we want from our practical reasoning.

What causes us the trouble is that “benefits” belongs to the matter and not the form of the syllogism. It goes into one of the terms, giving us one too many terms for our sorites.

One way of getting “benefits” out of the matter of the syllogism would be to treat it as syncategorematic. Thus in “humans benefit from dry food”, we could say, the subject is “humans” and the predicate is “dry food”, while “benefits” expresses the way in which the predicate belongs to the subject.

But does “benefits” then express the quantity or the quality of the proposition? Since the proposition appears straightforwardly affirmative, “benefits” does not seem to express a new quality. It might, then, express quantity. But how? In addition to saying dry food belongs to all humans and dry food belongs to some humans, can we also say that dry food belongs tobenefit humans?

This seems bizarre on the face of it, but there might be something in it. Michael Thompson’s Life and Actionproposes that in order to understand practical reasoning, we need a new “logical form”. From the way he describes it, what he seems to want is a new quantifier. To use Geach’s example, “acorns grow into trees” is a true proposition meaning neither thatall acorns grow into trees nor merely that some acorns grow into trees. The first is false; the second is not quite what is meant, since “grow into oaks” isn’t just something that happens to belong to acorns; it belongs to themessentially: it is part of the ‘life-form’ of acorns that they grow into oaks.

Most philosophers would say that the reference to ‘life-form’ here is categorematic; it expresses a non-logical relation between acorns and the activity of growing into oaks. But Thompson’s Hegelian proposal is that when we begin talking about living things, we introduce at least one newlogical form. There is a distinct logical relation between subject and predicate, when we predicate an activity that belongs to the ‘life-form’ of a living thing.

This works, I have proposed, like a quantifier. It is not that all acorns grow into oaks, nor merely that some acorns grow into oaks, nor even that mostacorns grow into oaks (they don’t). Rather, acorns grow into oaks ‘life-form-wise’, where the latter expression introduces a distinct quantifier not recognised in standard predicate or plurative logic.

In Aristotelian terms, it expresses a way in which the predicate belongs to the subject, a way that is neither universal nor particular.

This can, I think, be used to make sense of the Aristotelian practical syllogism. If we rush to the solution, here is what we might do. First, take “b” as a strange sort of belonging that a predicate can have to a subject, expressed by the word “benefits”. Now we can assign the terms of the sorites in this way:

A: humans

B: dry food

C: me

D: this bread

The form of the sorites will then be (taking the quantity of singular propositions to be universal): AbB, CaA, ∴CbB, DaB, ∴CbD. I represent the sorites again putting subjects in round brackets, predicates in square, and now syncategorematic terms in italics:

Benefit (human beings) [dry food]

All (I) [human being]

All (This bread) [dry food]

Benefit (I) [dry food]

Note that the form is the same as what it would be if the ‘quantity’-term “benefit” were replaced with “all”. But then we’d get the absurd conclusion that dry food belongs to me in the standard way that a predicate belongs to a subject — that “dry food” is either a class to which I belong or a property of me.

But since we have taken “benefit” out of the matter of the syllogism and placed it into the form, it can modify the copula. It modifies it by causing it to express a relation of benefiting rather than a relation of class-membership, identity, or predication.

This is extremely radical. It makes the relation of benefiting into a logical relation! And it is much more radical than what Thompson proposes. He wants activities to be predicated of subjects in the normal way, but subject to a strange quantifier.

We can get to something more like what he is after by going a bit more slowly. First, we replace “dry food” and “this bread” by “eating dry food” and “eating this bread”. We still need the extra quantifier, since what we want to say is that those activities belong to the subject in a very particular way, as pertaining to its ‘life-form’ and not just to some or all or most of its extension. But now it looks much more like a quantity-term than “benefits”, which seemed to change the relation of predication into something else entirely.

Suppose we use the adverb “ideally” to express this special sort of quantity (as we might say that “ideally” acorns grow into oak trees). The resulting sorites is:

Ideally (human beings) [eat dry food]

All (I) [human being]

All (Eat this bread) [eat dry food]

Ideally (I) [eat dry food]

The sorites would be equally valid if “ideally” were replaced by “all”, but then it wouldn’t look like a practical syllogism at all. The conclusion would be an assertion about what I do, whereas here the conclusion looks like a recommendation. And it would anyway be bad practical reasoning to move from what everyone does to what I ought to do: e.g., everyone screws up sometimes.

I do not mean to disagree with Anscombe, however (I rarely do). It is stillnot the case that it is the form that makes this syllogism practical. Having certain propositions in the form, “P belongs to S ideally” is a necessary but not a sufficient condition for a syllogism to be practical. Take, for instance, the syllogism:

Ideally swallows migrate for winter.

These birds are sparrows.

Therefore: Ideally they migrate for winter.

I might be using this inference to decide what to do, but I am more likely to be making a prediction about what the birds will do. It is still the case that what makes an inference practical is what we want to do with it and not its form as such. But now it is the case that practical inferences have to be of a certain form; they have to contain propositions of the right quantity.

Another question is whether an inference of the right form, of which I am the subject of the conclusion, is necessarily practical. Does a conclusion about what I ideally do have to involve some recommendation that I do something? Here moral philosophy begins, and I run away.